Today's accounting practice is primitive in its use of modern mathematics. It has the potential to greatly expand its horizons by easily applying the following mathematical tools to its double-entry system:
Linear Algebra and its application of vectors and matrices;
Graph Theory to related one account to another;
Statistics to visualize change and forecast trends;
Multi-dimensional analysis to provide deep research;
Signed numbers to allow for a true arithmetic.
Modern accounting practices have not really changed in 500 years, in which time mathematics has expanded exponentially. Accounting is a profession that requires a lot of skill but, unfortunately, very little imagination. All of the above mathematical tools could be utilized without changing any of the traditional practices of the profession. It would supplement the practice without challenging it.
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